The requirement is that at a given time, there must be only a single operator on a certain "desk".
And thus in the previous example the records with OPERATOR_ID = 2 and OPERATOR_ID = 3 are incompatible (they are overlapping).
How can I find all the incompatible records in table OPERATOR_LIST?

An index on (OPERATOR_ID, START_TIME, END_TIME) will help this along, but not indefinitely. If there are are thousands of entries for each operator, and thousands of operators, then this SQL might not scale very well. You could add hints to try to encourage a MERGE SEMI JOIN, which should make it scalable (but not exactly super fast).Ross Leishman